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Show that (n^2) + (n+1)^2 + (n+2)^2 = 3n^2 + 6n + 5, Hence show that the sum of 3 consecutive square numbers is always 2 away from a multiple of 3.

Expanding out the Brackets: (n 2 )+ (n 2 + n + n + 1) + (n 2 + 2n + 2n +4) = (n 2 ) + (n 2 +2n+1) + (n 2 +4n+4) =3n 2 + 6n +5 Using this result: Three consecutice numbers: n, n+1, n+2 So three consecutive sq...
JC
3739 Views

Solve the pair of simultaneous equations; (1) y + 4x + 1 = 0, (2) y^2 + 5x^2 + 2x = 0 .

Rearrage equation (1) to make y the subject of the formula. This gives y = -4x -1 . Substitute this value of y into equation (2). This gives (-4x -1)^2 +5x^2 +2x = 0 . Expanding out the brackets gives 16x^2 ...
MG
Answered by Melanie G. • Maths tutor
7523 Views

Outline Descartes’ ‘evil demon’ argument and explain what he says about knowledge of the self.

In the First Meditations, Descartes aims to determine which of his many beliefs amount to knowledge. Descartes argues that if there is any doubt regarding the truth of a proposition, one does not know that p...
AO
Answered by Angie O. • Philosophy tutor
145094 Views

Equilibrium of supply and demand

graph explanation, look at excess supply and excess demand, how increasing demand will lead to an increase in price and an increase in supply will lead to a decrease of the price. This will always converge t...
AB
Answered by Alex B. • Economics tutor
3399 Views

How can I make my experience of working in a retail store relevant to doing a Psychology (or any) degree?

example: On top of my A levels and hobbies this shows you can handle multiple things at once, which is a valuble skill at university , I have also worked part-time at a fast-food restaurant for more than a y...
AV
11852 Views